This is entirely possible, depending on which versions of the software you are currently using. Please let us know which releases of Microsoft office and Quicken you are using.
Your best bet would be to make a backup of your Windows 7 Operating system using Macrium Reflect which is free. Then I would update Windows 7 to windows 10 to see if your applications still work. Only then would I attempt using PC Mover pro to migrate the applications to the new Windows 10 machine.
Alternatively, once you confirm your apps work after upgrading Windows 7 upgrade to 10 you could make another backup image and restore that to the newly purchased computer. If you do this you will need to make a Macrium Rescue live boot USB.
Depending on the version of the software you have you have you might be able to install a fresh copy of the programs on the Windows 10 computer, which is always recommended over migrating from one machine to another.